"glance" (especially through a small opening), mid-15c., perhaps alteration of Middle English piken (see peek (v.)). Peeping Tom "a curious prying fellow" [Grose] is from 1796 (see Godiva).
"make a short chirp," c. 1400, probably altered from pipen (mid-13c.), ultimately imitative (compare Latin pipare, French pepier, German piepen, Lithuanian pypti, Czech pipati, Greek pipos).
"a furtive look, as if through a crevice, a glimpse," 1520s, originally and especially "the first looking out of light from the eastern horizon" (the sense in peep of day); from peep (v.1). General meaning "a furtive glance" is attested by 1730.
"short chirp," early 15c., from peep (v.2); meaning "slightest sound or utterance" (usually in a negative context) is attested from 1903. Meaning "young chicken" is from 1680s. The marshmallow peeps confection are said to date from 1950s.